Abel sum

Etymology
After Norwegian mathematician (1802-1829).

Noun

 * 1)  Given a power series $$f(x)= \sum_{n=0}^\infty a_n x^n$$ that is convergent for real x in the open interval (0, 1), the value $$\lim_{x \rightarrow 1^{-}} \sum_{n=0}^\infty a_n x^n$$, which is assigned to $$f(1)=\sum_{n=0}^\infty a_n$$ by the Abel summation method (or A-method).
 * 2) * 1967, Jan Mikusiński, Operational Calculus,, page 102,
 * The Abel sum of $$\textstyle\sum a_n$$ is defined as the limit of the corresponding power series:
 * $$\lim_{x \rightarrow 1-0} \sum_{n=0}^\infty a_n x^n$$.
 * The existence of the Abel sum is ascertained when the series in question is known to be summable (C, r) for some value of r.